Question

solve log (dy/dx)=2x+3y​

Answer 1

SOLUTION

TO SOLVE

$\displaystyle \sf{ log \bigg( \frac{dy}{dx} \bigg) = 2x + 3y}$

EVALUATION

$\displaystyle \sf{ log \bigg( \frac{dy}{dx} \bigg) = 2x + 3y}$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} = {e}^{2x + 3y}}$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} = {e}^{2x}. {e}^{ 3y}}$

$\displaystyle \sf{ \implies \: {e}^{ - 3y} \: dy = {e}^{2x} \: dx}$

On integration we get

$\displaystyle \sf{ \int{e}^{ - 3y} \: dy = \int {e}^{2x} \: dx}$

$\displaystyle \sf{ \implies \frac{{e}^{ - 3y} }{ - 3} = \frac{ {e}^{2x} }{2} + c}$

Where C is integration constant

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